Question

Twenty-five \(\mathrm{mL}\) of a \(0.388 \mathrm{M}\) solution of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is mixed with \(35.3 \mathrm{~mL}\) of \(0.229 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\). What is the molarity of the resulting solution? Assume that the volumes are additive.

Short answer

Answer: To find the molarity of the resulting solution, follow these steps: 1. Calculate the moles of solute in both solutions using the formula Moles = Molarity × Volume. 2. Add the moles of solute in both solutions to get the total moles of solute. 3. Calculate the total volume of the resulting solution by adding the volumes of both solutions. 4. Calculate the molarity of the resulting solution by dividing the total moles of solute by the total volume in liters.

Step-by-step solution

Calculate moles of solute in both solutions

First, we need to calculate the total moles of solute (Na2SO4) in each of the solutions. Recall that moles can be calculated as: Moles = Molarity × Volume For both solutions, we have: Moles of solute in first solution = \((0.388 \,\mathrm{M}) \times (25.0 \,\mathrm{mL})\) Moles of solute in second solution = \((0.229 \,\mathrm{M}) \times (35.3 \,\mathrm{mL})\)

Calculate total moles of solute

Now, we need to find the total number of moles of solute in both solutions by adding them together: Total moles = Moles of solute in first solution + Moles of solute in second solution

Calculate total volume of the resulting solution

According to the problem, the volumes are additive. So, to get the total volume of the resulting solution, simply add the volumes of both solutions: Total volume = Volume of first solution + Volume of second solution Total volume = \(25.0 \,\mathrm{mL} + 35.3 \,\mathrm{mL}\)

Calculate molarity of the resulting solution

Now, calculate the molarity of the resulting solution by dividing the total moles of solute by the total volume of the solution: Molarity = Total moles / Total volume Make sure to convert the volume from milliliters to liters by dividing it by 1000. Molarity = (Total moles) / (Total volume in liters)